I had a great experience with this text for start-to-finish self-study. My previous background with real analysis is limited to an upper-division course 30 years ago based on some of Apostol’s text, and a re-intro to math last year using Leon Simon’s Introduction to Multivariable Mathematics.
I worked through this text linearly, reading every section, studying every proof, and working every exercise (there are 777 of them), during a period of unassisted self-study lasting 7 months. The text is well-suited to this approach. The prose and proofs are direct and usually cite the more major / recent theorems to justify steps while leaving it to the reader to justify smaller steps. Examples are few but unusually useful. Insights and results that are useful or essential to completing a given exercise are just as likely to come from an earlier exercise as from an earlier theorem.
The few caveats I offer include the limited resolution of the printing (most pronounced with double subscripts) and the frequent typos in the latter chapters of the book (well beyond those listed in the single-page errata and associated website). I’d hazard a guess that beyond about chapter 10 (e.g. where Stanford's Math 171 syllabus leaves off), the text has not seen a lot of classroom use and thus not much typo feedback.
Foundations of Mathematical Analysis Paperback – 1 May 2010
- ASIN : B00KEVD5V6
- Publisher : Dover Publications, Inc.; 1st edition (1 May 2010)
- Language : English
- ISBN-10 : 0486477665
- ISBN-13 : 978-0486477664
- Customer reviews:
4.6 out of 5
20 global ratings
Top reviews from other countries
Great for self-studyReviewed in the United States on 28 October 2015
5 people found this helpful
As good for a reference as baby rudin and better for self-teaching first timerReviewed in the United States on 20 January 2014
Although it is necessary to master all the concepts and proof techniques of baby Rudin, this one is easier to follow if you are a first timer for advanced calculus. To really understand calculus, one need to learn the so called "advanced calculus", but if you are not major in math, just a serious math lover who wish to learn serious math, this book is a must have. This book is "compact", like baby Rudin, but the proofs are more straightforward in general. Besides, starting from real line and then generalized to metric space is a better approach for a first timer. Many analysis books use this approach, but most of them are not as "compact" as this book or baby Rudin.
10 people found this helpful
Very good bookReviewed in the United States on 23 February 2013
This is a very well written book, with an ample number of exercises of varying difficulty. I wouldn't say it reads like a novel. Few math books do. But it isn't so far away from that. The only reason I give it 4 stars rather than 5 (actually, my rating is more like 4.5 stars than 4, but I can't rate it that way), is that there are several spots where a few more words would have made things clearer instead of saying by theorem so and so this is true. Bottom line: the book is very good and is well worth the money. In fact, it is worth more! Good job authors!
9 people found this helpful
Love it.Reviewed in the United States on 18 August 2019
I love this book.
Who doesn't enjoy a good calculus from time to time?Reviewed in the United States on 16 July 2015
Only worked through the first half of this book, but it's been a pleasure thus far. Would be interested to see a bit on constructing the real numbers as seems to be all the rage with intro analysis books, but I'm not really an expert on this stuff (YET!) so take this minor criticism with a grain of salt. All in all, I wish my professor chose this as the textbook for our class.
3 people found this helpful